SOLUTION: Let f(x)=4x^2+5x+4 and let g(h)= f(1+h)−f(1)/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

Algebra ->  Functions -> SOLUTION: Let f(x)=4x^2+5x+4 and let g(h)= f(1+h)−f(1)/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      Log On


   

Question 1168270: Let f(x)=4x^2+5x+4 and let g(h)= f(1+h)−f(1)/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=1.
Enter the value of L:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Let f%28x%29=4x%5E2%2B5x%2B4 and let+g%28h%29=+%28f%281%2Bh%29-f%281%29%29%2Fh
Determine each of the following:
(a) g%281%29=
g%281%29=+%28f%281%2B1%29-f%281%29%29%2F1=f%282%29-f%281%29
f%282%29=4%2A2%5E2%2B5%2A2%2B4=16%2B10%2B4=30
f%281%29=4%2A1%5E2%2B5%2A1%2B4=4%2B5%2B4=13
=> g%281%29=30-13=17


(b) g%280.1%29=%28f%281%2B0.1%29-f%281%29%29%2F0.1=10f%281.1%29+-+10f%281%29
10f%281.1%29=10%2A%284%281.1%29%5E2%2B5%281.1%29%2B4%29=143.4
10f%281%29=10%2A%284%281%29%5E2%2B5%281%29%2B4%29=130
g%280.1%29=143.4-130=13.4+

(c) g%280.01%29=
similarly
g%280.01%29+=+100+f%281.01%29+-+100+f%281%29
100+f%281.01%29=100+%284%281.01%29%5E2%2B5%281.01%29%2B4%29=1313.04
100+f%281%29=100+%284%281%29%5E2%2B5%281%29%2B4%29=1300
g%280.01%29=1313.04-1300=13.04


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%28h%29 as h approaches 0 and is also called the derivative of f%28x%29 at the point when x=1.

lim%28h-%3E0%2C%28f%281+%2B+h%29+-+f%281%29%29%2Fh+%29= f'%281%29


derivative of f%28x%29=4x%5E2%2B5x%2B4+ is
f'%28x%29=8x%2B5..........at the point when x=1 is
f'%281%29=8%2A1%2B5=13

so, the value of L is: 13

as you can see, 17, 13.4 , 13.04 are getting closer and closer to 13