22. Given g(x)=2x3−x2−5x, with g(−2)=−10. Find f′(−10), where g−1(x)=f(x).
Answer is: option1
Solution:
We are asked to find f′(−10), where g−1(x)=f(x). From the inverse derivative rule:
f′(y)=1g′(x)wherey=g(x)
For g(x)=2x3−x2−5x, we differentiate:
g′(x)=6x2−2x−5
At x=−2:
g′(−2)=6(−2)2−2(−2)−5=6(4)+4−5=24+4−5=23
Since g(−2)=−10, we have:
f′(−10)=1g′(−2)=123
The correct answer is: a) 123
