AP Calculus AB / Differentiation Composite, Implicit, and Inverse Functions / Question No. 3

3. Let $f$ be the function given by $f (x) = 5 e^{3 x^{3}}$ . For what positive value of $a$ is the slope of the line tangent to the graph of $f$ at $(a, f (a))$ equal to 6?

0.142

0.344

0.393

0.595

Answer is: option2

0.344

Solution:

Slope of line tangent = $f^{'} (a) = 6$

$f^{'} (x) = 45 x^{2} e^{3 x^{2}} = 6$

Now, graph and find the zeroes of

$45 x^{2} e^{3 x^{2}} - 6 = 0$

$x = 0.344$

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