Question

(1 point) Let f(x) = 4x² + 5x +4 and let g(h) = (f(3+h)-f(3))/h

Determine each of the following:
(a) g(1) =
(b) g(0.1) =
(c) g(0.01) =
You will notice that the values that you entered are getting closer and closer to a number L. This number is called the limit of g(h) as h approaches 0 and is also called the derivative of f(x) at the point when x = 3. We will see more of this when we get to the calculus textbook.
(d)Enter the value of L:______

Answer 1

Answer: 33, 29.4, 29.04, 29

Explanation:

`f(3+h)=4(3+h)^2 +5(3+h)+4\\\\=4(h^2 +6h+9)+15+5h+4\\\\=4h^2 +24h+36+15+5h+4\\\\=4h^2 +29h+55\\\\\\f(3)=4(3)^2 +5(3)+4=36+15+4=55\\\\g(h)=(4h^2 +29h+55-55)/(h)\\\\=(4h^2 +29h)/(h)\\\\=4h+29\\\\\implies g(1)=33, g(0.1)=29.4, g(0.01)=29.04\\\\\implies L=29`