Find and Simplify the difference quotient

Question

f(3+h)-f(3)/h for the function f(x)=-4x^2-7

thanks again

Answer 1

Someone sure wants you to learn what derivatives are about
f(3+h) = -4(3+h)^2 -7
f(3+h) = -4(9 + 6h + h^2 ) - 7
f(3+h) = -36 - 24 h - 4 h^2 - 7
f(3) = -36 - 7
f(3+h) - f(3) = -24 h - 4 h^2
divide by h
-24 - 4 h

NOTE AGAIN
lrt h--->0
you get slope = -24

which is the value of the derivative (which is -8 x) at x = 3 !!!!