Consider the following function.f(x) = x2 + 3.5x − 6(a) Write the derivative formula.f '(x) = 2x+3.5 (b) Locate any relative extreme points. (If an answer does not exist, enter DNE.)relative maximum      (x, y) = relative minimum (x, y) =

(b) Locate any relative extreme points. (If an answer does not exist, enter DNE.) relative maximum (x, y) = relative minimum (x, y) =

Estimate the input value(s) where the function has a relative extreme point. Identify each relative extreme as a maximum or minimum, and indicate whether the derivative of the function at that point is zero or does not exist.input value maximumor minimum? derivativex = (smaller value) x = (larger value)

Suppose that it is given to you that f′(x)=(x+5)(6−x)(x−9) Then the first relative extremum (from the left) for f(x) occurs at x= The function f(x) has a relative ? at this point. The second relative extremum (from the left) for f(x) occurs at x= The function f(x) has a relative ? at this point. The third relative extremum (from the left) for f(x) occurs at x= The function f(x) has a relative ? at this point. The first inflection point (from the left) for f(x) occurs at x= The second inflection point (from the left) for f(x) occurs at x=

For the given function, find the requested relative extrema or extreme value (without a calculator).y = xe4x; relative extrema

Use the first derivative test to find the two critical points of the function. First point:(Either of the points can be 𝑥1 or 𝑥2.)𝑥1= Relative Maximum Relative Minimum Neither