Question

In: Math

consider the function f(x) = 1 + x3  e-.3x a. what is f'(x) b. what is f''(x)...

consider the function f(x) = 1 + x3  e-.3x

a. what is f'(x)

b. what is f''(x)

c. what are the critical points of f(x)

d. are the critical points a local min or local max or neither?

e. find the inflection points

f. if we define f(x) to have the domain of [2,50] compute the global extreme of f(x) on that interval

Solutions

Expert Solution


Related Solutions

Consider the following functions. g(x) =x3 − 10x h(x)=4x2 + 3x f(x)=(x3 − 10x)(4x2 + 3x)...
Consider the following functions. g(x) =x3 − 10x h(x)=4x2 + 3x f(x)=(x3 − 10x)(4x2 + 3x) Find the derivative of each function. g '(x)= h '(x)= f '(x)=
Consider the function f(x)= x3 x2 − 1 Express the domain of the function in interval...
Consider the function f(x)= x3 x2 − 1 Express the domain of the function in interval notation: Find the y-intercept: y=   . Find all the x-intercepts (enter your answer as a comma-separated list): x=   . On which intervals is the function positive?   On which intervals is the function negative?   Does f have any symmetries? f is even;f is odd;     f is periodic;None of the above. Find all the asymptotes of f (enter your answers as equations): Vertical asymptote (left):   ; Vertical...
For this problem, consider the function f(x) = x3 - 9x2 +15x + 3.
  For this problem, consider the function f(x) = x3 - 9x2 +15x + 3. A. Determine the intervals on which f(x) is increasing and intervals on which f(x) is decreasing. B. Determine all relative (local) extrema of f(x). C. Determine intervals on which f(x) is concave up and intervals on which f(x) is concave down. D. Determine all inflection points of f(x).
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) _______
1.Consider the function: f(x, y) = 2020 + y3-3xy + x3. a) Find fx(x, y), and...
1.Consider the function: f(x, y) = 2020 + y3-3xy + x3. a) Find fx(x, y), and fye(x, y). b) Find all critical points of f(x, y). c) Classify the critical points of f(x, y) (as local max, local min, saddle). 2.Consider f(x) = 2x-x2and g(x) = x2 a) [2 points] Find the intersection points (if any) of the graphs of f(x) and g(x). b) [4 points] Graph the functions f(x) and g(x), and shade the region bounded by: f(x), g(x),...
1. The function f(x, y) = ln(x3 + 2) / (y2 + 3) (this function is...
1. The function f(x, y) = ln(x3 + 2) / (y2 + 3) (this function is of a fraction format) : a. has a stationary point at (1, 0) b. has a stationary point at (0, 0) c. has a stationary point at (0, 1) d. has no stationary points 2. Which of the following functions don’t have unit elasticity at P = 6? a. Demand: Qd = 24 - 2 P b. Demand: Qd = 10/P c. Demand: log...
The function f(x)=3x+2 is one-to-one a) find the inverse of f b) State the domain and...
The function f(x)=3x+2 is one-to-one a) find the inverse of f b) State the domain and range of f c) State the domain and range of f-1 d) Graph f,f-1, and y=x on the same set of axes
Consider the function f(x) = 3/(3x+ 4), c= 0 a)Find the power series for the function...
Consider the function f(x) = 3/(3x+ 4), c= 0 a)Find the power series for the function centered at c b)Determine the interval of convergence
Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = e^(3x) +...
Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = e^(3x) + e^(−x) (a) Find the interval on which f is increasing. (Enter your answer using interval notation.) Find the interval on which f is decreasing. (Enter your answer using interval notation.) (b) Find the local minimum and maximum values of f. local minimum value local maximum value (c) Find the inflection point. (x, y) = Find the interval on which f is concave up. (Enter...
Consider the function f = x + 6cos(3x) + 5sin(x) +5 has at least one zero...
Consider the function f = x + 6cos(3x) + 5sin(x) +5 has at least one zero for all real numbers. Why?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT