Find the critical point and the interval on which the given function is increasing or decreasing, and apply the First Derivative Test to the critical point. Let f(x) = 7x2 + 5.

Is f a maximum or minimum at the critical point?

Find the interval on the left of the critical point.

On this interval, f is

a. increasing

b. decreasing

while f is

a. positive

b. negative

Find the interval on the right of the critical point.

On this interval, f is

a. increasing

b. decreasing

while f is

a. positive

b. negative

critical point is 0

f is maximum because at the critical point we substitute x = 0 at the derivative

Step-by-step explanation:

the critical point is at the point x= 0 after taking the derivative, we equate it to zero and the result is 0.

f is maximum because at the critical point we substitute x = 0 at the derivative  we have 5 > 0

the interval on the left of the critical point is - infinity < f< 0

on this interval increasing while f is negative

on the right of critiocal point 0 >= f < +infinity

on this interval f is increasing while f is positive.

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