Which AP Practice Question Choice Did You Select?

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SUMMARY

The forum discussion centers on solving a practice AP calculus question involving the chain rule. The participant initially selected option (D) but later confirmed that the correct answer is (B), calculated by applying the chain rule to the function $$h(x)=f\left(g(x)\right)$$. By differentiating and substituting $$x=1$$, they found that $$h'(1) = -5 \cdot -3 = 15$$, leading to the correct choice. The discussion highlights the importance of understanding the chain rule in calculus.

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karush
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this is a practice AP question but the answer is not given from the A to E selection
had a hard time with this not knowing what the functions were so just using what was given I did this (bold mine) I chose (D). It appeared that some of what was give was not needed...
 
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We are given:

$$h(x)=f\left(g(x) \right)$$

Thus, by the chain rule, we find:

$$h'(x)=f'\left(g(x) \right)\cdot g'(x)$$

So, plug in $x=1$, and what do you find?
 
MarkFL said:
We are given:

$$h(x)=f\left(g(x) \right)$$

Thus, by the chain rule, we find:

$$h'(x)=f'\left(g(x) \right)\cdot g'(x)$$

So, plug in $x=1$, and what do you find?

$$-5\cdot-3 = 15$$ which is $$(B)$$
 
Correct! (Star)
 
thanks
don't see the thanks button tho?
 

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