Find f '(−3), if f(x) = (2x^2 − 7x)(−x^2 − 7). round your answer to the nearest integer. use the hyphen symbol, -, for negative values.

Step by step:

To get the derivative you can either multiply out the product (which I did below), or apply the formula for the derivative of a product of two functions. Either way you will obtain the same result, of course.

use product rule

(where the ' symbol is derivitive with respect to x, (just using Leibniz notation)

also remember the power rule:

and sum rule,

so first find the derivitive then evaluate it

if we say that and

setup:

find g'(x) and h'(x)

so

evaluate f'(-3)

f'(-3)=538

the answer would be d.

step-by-step explanation:

move all variables to the left side and all constants to the right side

(x−3)^2+(y−1)^2=16

this is the form of a circle. use this form to determine the center and radius of the circle.

( x − h ) 2 + ( y − k ) 2 = r 2

match the values in this circle to those of the standard form. the variable   r   represents the radius of the circle,   h   represents the x-offset from the origin, and   k   represents the y-offset from origin.

r = 4

h = 3

k = 1

the center of the circle is found at   ( h , k ) .

center:   ( 3 , 1 )

these values represent the important values for graphing and analyzing a circle.

center:   ( 3 , 1 ).

radius:   4