Answer:
9. (a) -4.58872425
10. (a) -18.22610955
Explanation:
You want the approximate value of f'(5.245) if f(x) = ln(3x) +sin(5x -4) -3 and the approximate value of f''(2.156) if f(x) = 2tan(x) +cos(2x) using h = 0.025 and 0.003, respectively.
9. f'(5.245)
The approximate value of f'(x) is the difference quotient ...
f'(x) ≈ (f(x+h) -f(x))/h
For x=5.245 and h=0.025, this is ...
f'(x) ≈ ((f(5.245 +0.025) -f(5.245))/0.025
The calculator screen in the first attachment shows the value of this is about ...
f'(5.245) ≈ -4.58872425
10. f''(2.156)
For the second derivative, we use ...
f'(x) ≈ ((f(x +h) -f(x))/h
f''(x) = (f'(x -h) -f'(x))/h
The calculator screen in the second attachment shows the calculations and the final value of f''(2.156) as ...
f''(2.156) ≈ -18.22610955
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Additional comment
Note that the calculator must be set to radians mode.
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