Assume f and g are differentiable on their domains with h

Jason Yuhas 2021-12-17 Answered
Assume f and g are differentiable on their domains with h(x)=(fog)(r). Suppose the equation of the line tangent to the graph of g at the point (4,7) isy=3x5 and the equation of the line tangent to the graph of f at (7,9) is y=2x+23.
(a) Calculate h(4) and h(4).
(b) Determine an equation of the line tangent to the graph of h at the point on the graph where x=4.
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Melinda McCombs
Answered 2021-12-18 Author has 38 answers
Step 1:Define the functionsNSk(a)
Since h(4)=f(g(4)) and h(4)=f(g(4)).g(4) , therefore, to determine the value of h(4) and h(4) : we need to know the values of g(4),f(g(4)),g(4) and f(g(4)) .
Now, (4,7) point lies on the graph of g, therefore, g(4)=7.
Similarly, (7,9) lies on graph f , therefore, f(7)=9.
Now, g(4)=7 , therefore, f(g(4))=9.
We know that if a line is tangent to a graph at a point (x,y), then differentiation of the function will have the same value to the slope of the line.
Now, slope of the line : y=3x5 is 3.
As the the line y=3x5 is tangent to the graph g on (4,7), therefore, g(4)=3.
Similarly,
we have, slope of the line y=2x+23 is -2 .
Therefore, f(7)=2.
Therefore, f(g(4))=2.
So,
h(4)=f(g(4))=9.
And,
h(4)=f(g(4)).g(4)=2.3=6.

We have step-by-step solutions for your answer!

Neil Dismukes
Answered 2021-12-19 Author has 37 answers
Step 2: Second Part
(b)
Using the formula of tangent , we have :
yh(4)=h(4).(x4) [atx=4]
y9=(6).(x4)
y=6x+33.
Therefore, equation of the tangent line is :
y=6x+33.

We have step-by-step solutions for your answer!

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more