3. Let \( f \) be the function given by \( f(x) = 5e^{3x^3} \). 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?
Answer is: option2
Solution:
Slope of line tangent = \( f'(a) = 6 \)
\( f'(x) = 45x^2 e^{3x^2} = 6 \)
Now, graph and find the zeroes of
\( 45x^2 e^{3x^2} - 6 = 0 \)
\( x = 0.344 \)
