Given the function f(x)=2x3−15x2 over the interval −1≤x≤6, answer the following questions. (a) Find f′(x) and f′′(x). f′(x)= f′′(x)= (b) Find the critical points of f. Enter the exact answers in increasing order. x1= x2= (c) Find any inflection points of f. Enter the exact answer.

Step-by-step explanation:

Consider the function over the given interval.

a)Recall that the following derivatives' properties:

-

-(f+g)' = f'+g' when f and g are differentiable

-(cf)' = cf', where c is a constant and f a differentiable function.

Then, using this properties we have that

b) Recall that a critical point of a function f is where it's derivatives are 0 or they don't exist. From point a we have that both f' and f'' are polynomials, so the derivatives are continous. Hence,the critical points are where the first derivative is equal to zero.

Then, we have the following equation

Hence, the only critical points are x=0 and x=5.

c) Recall that the inflection points are were f''(x) is zero. Then, we have the following equation

The solution of this equation is

so x=2.5 is an inflection point of the function f

the anwser is d) 75°

step-by-step explanation:

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is