Q12 f(x) x + 1 the derivative of f on the interval [-2, 7] is given below. Define g(x)= = 5 4- 3-- 2 1 21, -2- where f is a continuous function with f(2)=-1. The graph of y f'(x) 12 3 4 5 X
![Q12
f(x)
Define g(x)
x + 1
the derivative of f on the interval [-2, 7] is given below.
where f is a continuous function with f(2)=-1. The graph of
y
5
4
f'(x)
3
A
2
-1
+2 =1
1 2 3 4 5
2
An equation of the line tangent to the graph of g(x) at x = 2 is
X](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2cc04b1e-803c-4d9d-b550-d2ae04bcc2b3%2F5af122e4-30d2-4d89-b4e0-9bfdce2e2508%2Fswivcii_processed.jpeg&w=3840&q=75)
We know that where f is a continuous function with f (2) = - 1 and we also have the plot of f'(x) in the interval [-2,7].
Required to find the equation of the tangent of g(x) at x=2
let's find the derivate of g(x)
At x = 2 we get
from given data we have
From graph of f'(x) we get
Now the tangent equation is ----(1)
where m is slope of the tangent line . That is
(1) -----(2)
At x = 2 we have = y
From (2) we get
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