Find the derivatives of each of the following functions: 1. f(x) = (3x^2 + 2x −...

Find the derivatives of each of the following functions:

1. f(x) = (3x^2 + 2x − 7)^5 (2x + 1)^8

2. g(t) = cos(e^2x2+8x−3)

3. h(x) = e^x2/tan(2x−3)

4. Find dy/dx if cos(xy) = x^2y^5

Expert Solution

milcah answered 2 years ago

Find all functions f(x) with f′′(x) = 3x^3 − 2x^2 + x, f(0) = 1, and...

Find all functions f(x) with f′′(x) = 3x^3 − 2x^2 + x, f(0) = 1, and f(1) = 1.

For the function f(x) = x^2 +3x / 2x^2 + 6x +3 find the following, and...

For the function f(x) = x^2 +3x / 2x^2 + 6x +3 find the following, and use it to graph the function. Find: a)(2pts) Domain b)(2pts) Intercepts c)(2pts) Symmetry d) (2pts) Asymptotes e)(4pts) Intervals of Increase or decrease f) (2pts) Local maximum and local minimum values g)(4pts) Concavity and Points of inflection and h)(2pts) Sketch the curve

For the function f(x) = x^2 +3x / 2x^2 + 7x +3 find the following, and...

For the function f(x) = x^2 +3x / 2x^2 + 7x +3 find the following, and use it to graph the function. Find: a)(2pts) Domain b)(2pts) Intercepts c)(2pts) Symmetry d) (2pts) Asymptotes e)(4pts) Intervals of Increase or decrease f) (2pts) Local maximum and local minimum values g)(4pts) Concavity and Points of inflection and h)(2pts) Sketch the curve

1. Find the critical numbers for the following functions (a) f(x) = 2x 3 − 6x...

1. Find the critical numbers for the following functions (a) f(x) = 2x 3 − 6x (b) f(x) = − cos(x) − 1 2 x, [0, 2π] 2. Use the first derivative test to determine any relative extrema for the given function f(x) = 2x 3 − 24x + 7

A. In the following parts, consider the function f(x) =1/3x^3+3/2x^2−4x+ 7 (a)Find the intervals on which...

A. In the following parts, consider the function f(x) =1/3x^3+3/2x^2−4x+ 7 (a)Find the intervals on which f is increasing/decreasing and identify any local extrema. (b) Find the intervals on which f is concave up/down and find any inflection points. B. Consider the function f(x) = sin(x) + cos(x). Find the absolute minimum and absolute maximum on the interval [−π,π].

find f'(x) 1. f(x)=3sinx-secx+5 ___ 2. f(x)=e^xcot(3x) _ 3. f(x)= cos^5(3x-1) _____

find f'(x) 1. f(x)=3sinx-secx+5 _______ 2. f(x)=e^xcot(3x) _______ 3. f(x)= cos^5(3x-1) _______

Find the Taylor series for f (x) = 2/(1+3x) at x = a where a =...

Find the Taylor series for f (x) = 2/(1+3x) at x = a where a = 0

T(1+2x)=1+x-x^2 T(1-x^2)=2-x T(1-2x+x^2)=3x-2x^2 a)compute T(-6x+3x^2) b) find basis for N(T), null space of T c) compute...

T(1+2x)=1+x-x^2 T(1-x^2)=2-x T(1-2x+x^2)=3x-2x^2 a)compute T(-6x+3x^2) b) find basis for N(T), null space of T c) compute rank of T and find basis of R(T)

Solve for x x^4 + 2x^3 + 2x^2 + 3x + 1 = 0

find the general solution (2x+3)dy/dx=(2x+3)/(x^2 +3x+1) -y

Question