please show your work

h(x)=f(g(x)) is a differentiable function

if x=2.5, f'(x)=3.85

if x=2.7, f'(x)=3.97

if x=2.9, f'(x)=4.03

if x=1.3, g(x)=2.5

if x=1.35, g(x)=2.7

if x=1.40, g(x)=2.9

in Calculus Answers by
edited

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

3+3x3-3+3=
3+3x3-3+3=

Question: Using the following values, find the approximate value of h'(x) at x=1.35.

Where h(x) = f(g)(x).

Here we use the chain rule.

If h(x) = f(g) and g() is a function of x, then

dh/dx = (df/dg).(dg/dx)

To find h'(x) at x = 1.35,

we need h'(x) = (df(g)/dg).(dg(x)/dx)

at x = 1.35, g'(x=1.35) = ??

at x = 1.35, g(x=1.35) = 2.7

at g = 2.7, f'(g=2.7) = 3.97

We don't have information on the value(s) of g'(x) for various values of x, but we do have information on the variation of g(x) for different values of x, which shows that g(x) is a straight line function which works out as

g(x) = 4x - 2.7

so, g'(x) = 4. i.e. g'(x=1.35) = 4.

Now we have g'(x=1.35) = 4 and f'(g=2.7) = 3.97,

So h'(x=1.35) = (df(g=2.7)/dg).(dg(x=1.35)/dx) = 3.97*4 = 15.88

Answer: 15.88

by Level 11 User (81.5k points)

Related questions

1 answer
asked Mar 12, 2014 in Calculus Answers by math, math problem, calculus, calculus p | 557 views
1 answer
1 answer
1 answer
1 answer
asked Apr 8, 2020 in Calculus Answers by qwertykl Level 2 User (1.4k points) | 1.5k views
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
87,124 questions
96,997 answers
2,371 comments
24,433 users