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Use a computer microscope to determine the following value, correct to 1 decimal

ID: 3143494 • Letter: U

Question

Use a computer microscope to determine the following value, correct to 1 decimal place. Obtain estimates using a sequence of windows, and shrink the field of view until the first 2 decimal places stabilize. Show all the estimates you constructed in each sequence.

a) f'(1) where f(x)=x^4 - 8x

b) h'(0) where h(s) = 3^s

c) The slope of the graph of w = sin z at z = /4

d) The slope of the graph of y = t+2^(-t) at t = 7

e) The slope of the graph of y = x^(2/3) at x = -5

Use a computer microscope to determine the following values, correct to 1 decimal place. Obtain estimates using a sequence of windows, and shrink the field of view until the first 2 decimal places stabilize. Show all the estimates you constructed in each sequence. f'(1) where f(x) = x^4 - 8x. h'(0) where h(s) = 3^s. The slope of the graph of w = sin z at z = pi/4. The slope of the graph of y = t + 2^-t at t = 7. The slope of the graph of y = x^2/3 at x = -5.

Explanation / Answer

a) f'(x) = 4x3 - 8 = 4.0 - 8.0 = -4.0

b) h'(s) = 3s ln(3) = ln (3) = 0.5

c) w' = cos z = cos (/4) = 0.7

d) y' = 1 - 2-t ln (2) = 1.0

e) y' =  2/3 x-1/3 = -0.4

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