Explained: "Find the first and second derivatives of the..." - Plainmath

aramutselv

Answered question

2021-12-06

Find the first and second derivatives of the function.

h (t) = t^{4} - 9 t^{3} + 4 t^{2} - 6 t - 13

h'(t)=
h''(t)=

Answer & Explanation

Hattie Schaeffer

Beginner2021-12-07Added 37 answers

Step 1
The given function is

h (t) = t^{4} - 9 t^{3} + 4 t^{2} - 6 t - 13

.
Obtained the first derivative of the function

h (t) = t^{4} - 9 t^{3} + 4 t^{2} - 6 t - 13

as follows:

h^{'} (t) = \frac{d}{d t} (t^{4} - 9 t^{3} + 4 t^{2} - 6 t - 13)

= 4 t^{4 - 1} - 9 (3 t^{3 - 1}) + 4 (2 t^{2 - 1}) - 6 (t^{1 - 1}) - 0

= 4 t^{3} - 27 t^{2} + 8 t - 6

Step 2
Obtain the second derivative of the function

h (t) = t^{4} - 9 t^{3} + 4 t^{2} - 6 t - 13

as follows:

h^{″} (t) = \frac{d}{d t} (4 t^{3} - 27 t^{2} + 8 t - 6)

= 4 (3 t^{3 - 1}) - 27 (2 t^{2 - 1}) + 8 (t^{1 - 1}) - 0

= 12 t^{2} - 54 t + 8

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