Let f (x) = 12x^5 + 15x^4 − 40x^3 + 1, defined on R. (a) Find...

Let f (x) = 12x^5 + 15x^4 − 40x^3 + 1, defined on R.

(a) Find the intervals where f is increasing, and decreasing.

(b) Find the intervals where f is concave up, and concave down. (c) Find the local maxima, the local minima, and the inflection points.

(d) Find the Maximum and Minimum Absolute of f over [−2, 2].

Expert Solution

milcah answered 2 years ago

f(x) = 15x^4-3x^5 / 256. f'(x) = 60x^3 - 15x^4 / 256 f''(x) = 45x^2 -...

f(x) = 15x^4-3x^5 / 256. f'(x) = 60x^3 - 15x^4 / 256 f''(x) = 45x^2 - 15x^3 / 64 Find the horizontal and vertical asymptotes Find the local minimum and maximum points of f(x) Find all inflection points of f(x)

Let f(x) = -2x3 - 9x2 - 12x + 3. Find the following: a) The domain...

Let f(x) = -2x3 - 9x2 - 12x + 3. Find the following: a) The domain of f Answer can be an interval or in words b) The y-intercept Answer must be a point c) f '(x) d) The critical numbers, if any. e) The open interval(s) where the function is increasing and the open interval(s) where the function is decreasing. The answer to this question will be accepted in one of two ways: 1) Show the number line with...

6. (a) let f : R → R be a function defined by f(x) = x...

6. (a) let f : R → R be a function defined by f(x) = x + 4 if x ≤ 1 ax + b if 1 < x ≤ 3 3x x 8 if x > 3 Find the values of a and b that makes f(x) continuous on R. [10 marks] (b) Find the derivative of f(x) = tann 1 1 ∞x 1 + x . [15 marks] (c) Find f 0 (x) using logarithmic differentiation, where f(x)...

5. (a) Let f : R \ {−1} → R, f(x) = x+1. Show that f...

5. (a) Let f : R \ {−1} → R, f(x) = x+1. Show that f is injective, but not surjective. (b) Suppose g : R\{−1} → R\{a} is a function such that g(x) = x−1, where a ∈ R. Determine x+1 a, show that g is bijective and determine its inverse function.

1. Find the critical numbers of the function f (x) = x^3− 12x in the interval...

1. Find the critical numbers of the function f (x) = x^3− 12x in the interval [0, 3]. Then find the absolute maximum and the absolute minimum of f(x) on the interval [0,3]. 2. Using only the limit definition of derivative, find the derivative of f(x) = x^2− 6x (do not use the formulas of derivatives).

Find f 1)f”(x)=-2+12x-12x(Square), f’(0)=12 F(x)=? 2)Find a function f such that f’(x)=5x cube and the line...

Find f 1)f”(x)=-2+12x-12x(Square), f’(0)=12 F(x)=? 2)Find a function f such that f’(x)=5x cube and the line 5x+y=0 is the tangent to the graph of f F(x)=? 3)A particle is moving with the given data. Find the position of the particle a(t)=11sin(t)+4cos(t), s(0)=0, s(2pi)=16 s(t)=? (please i need help)

Find f. f ''(x) = 4 − 12x, f(0) = 6, f(2) = 10

Suppose f is defined by f(x)=3x/(4+x^2), −1≤x<3. What is the domain of f? Find the intervals...

Suppose f is defined by f(x)=3x/(4+x^2), −1≤x<3. What is the domain of f? Find the intervals where f is positive and where f is negative. Does f have any horizontal or vertical asymptotes. If so, find them, and show your supporting calculations. If not, briefly explain why not. Compute f′ and use it to determine the intervals where f is increasing and the intervals where f is decreasing. Find the coordinates of the local extrema of f Make a rough...

Let f(x,y) = 3x3 + 3x2 y − y3 − 15x. a) Find and classify the...

Let f(x,y) = 3x3 + 3x2 y − y3 − 15x. a) Find and classify the critical points of f. Use any method taught during the course (the second-derivative test or completing the square). b) One of the critical points is (a,b) = (1,1). Write down the second-degree Taylor approximation of f about this point and motivate, both with computations and with words, how one can see from this approximation what kind of critical point (1,1) is. Use completing the...

Let f(x,y) = 3x3 + 3x2 y − y3 − 15x. a) Find and classify the...

Let f(x,y) = 3x3 + 3x2 y − y3 − 15x. a) Find and classify the critical points of f. Use any method taught during the course (the second-derivative test or completing the square). b) One of the critical points is (a,b) = (1,1). Write down the second-degree Taylor approximation of f about this point and motivate, both with computations and with words, how one can see from this approximation what kind of critical point (1,1) is. Use completing the...

Question

Let f (x) = 12x^5 + 15x^4 − 40x^3 + 1, defined on R. (a) Find...

Solutions

Expert Solution

Related Solutions

f(x) = 15x^4-3x^5 / 256. f'(x) = 60x^3 - 15x^4 / 256 f''(x) = 45x^2 -...

Let f(x) = -2x3 - 9x2 - 12x + 3. Find the following: a) The domain...

6. (a) let f : R → R be a function defined by f(x) = x...

5. (a) Let f : R \ {−1} → R, f(x) = x+1. Show that f...

1. Find the critical numbers of the function f (x) = x^3− 12x in the interval...

Find f 1)f”(x)=-2+12x-12x(Square), f’(0)=12 F(x)=? 2)Find a function f such that f’(x)=5x cube and the line...

Find f. f ''(x) = 4 − 12x, f(0) = 6, f(2) = 10

Suppose f is defined by f(x)=3x/(4+x^2), −1≤x<3. What is the domain of f? Find the intervals...

Let f(x,y) = 3x3 + 3x2 y − y3 − 15x. a) Find and classify the...

Let f(x,y) = 3x3 + 3x2 y − y3 − 15x. a) Find and classify the...