The value of the derivative at x = 11 is 8/121
The equation of the function is given as:
[tex]f(x) = -\frac 8x[/tex]
Rewrite the above equation as:
[tex]f(x) = -8x^{-1}[/tex]
Using the first principle, the derivative of f(x) is:
[tex]f'(x) = -1 \times -8x^{-1-1}[/tex]
[tex]f'(x) = -1 \times -8x^{-2}[/tex]
Evaluate the product
[tex]f'(x) = 8x^{-2}[/tex]
Rewrite the above equation as:
[tex]f'(x) = \frac{8}{x^2}[/tex]
Substitute 11 for x
[tex]f'(11) = \frac{8}{11^2}[/tex]
[tex]f'(11) = \frac{8}{121}[/tex]
Hence, the value of the derivative at x = 11 is 8/121
Read more about function derivatives at:
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