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PLEASEEE HELP!!! Let f and g be differentiable functions such that f' (1) = 2 and g’ (1) = 6. If h (x) = 5 f(x) - 4g (x) + 3x^2 - 2, what is the value of h’ (1) ?

PLEASEEE HELP Let f and g be differentiable functions such that f 1 2 and g 1 6 If h x 5 fx 4g x 3x2 2 what is the value of h 1 class=

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Hi! Attached is my work on how to solve it. Feel free to ask any questions about anything you’re confused about!
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abidemiokin

The value of h'(1) is -8

Given the following expression;

[tex]h (x) = 5 f(x) - 4g (x) + 3x^2 - 2[/tex]

Differentiating the function above:

[tex]h' (x) = 5 f'(x) - 4g' (x) + 6x[/tex]

Given the following parameters

[tex]f' (1) = 2\\g' (1) = 6[/tex]

Get h'(1)

[tex]h' (1) = 5 f'(1) - 4g' (1) + 6(1)\\h' (1)=5 (2) - 4(6) + 6(1)\\h' (1)= 10-24+6\\h' (1)=-8[/tex]

Hence the value of h'(1) is -8

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