Exam 1

  1. Question

    What is the derivative of f(x)= x8 e3.4x , evaluated at x=0.8?

    1. 25.47
    2. 34.13
    3. 38.76
    4. 28.02
    5. 28.97

    Solution

    Using the product rule for f(x)=g(x)·h(x), where g(x):= x8 and h(x):= e3.4x , we obtain
    f'(x) = [g(x)·h(x)]'=g'(x)·h(x)+g(x)·h'(x) = 8 x8-1 · e3.4x + x8 · e3.4x ·3.4 = e3.4x ·(8 x7 +3.4 x8 ) = e3.4x · x7 ·(8+3.4x).

    Evaluated at x=0.8, the answer is
    e3.4·0.8 ·0. 87 ·(8+3.4·0.8)=34.127595.

    Thus, rounded to two digits we have f'(0.8)=34.13.

    1. False
    2. True
    3. False
    4. False
    5. False