21. let f and g be differentiable functions such that f(1) = 2 and g(1) = 6. if h(x) = 5f(x) - 4g(x) + 3x²…

21. let f and g be differentiable functions such that f(1) = 2 and g(1) = 6. if h(x) = 5f(x) - 4g(x) + 3x² - 2, what is the value of h(1)?

21. let f and g be differentiable functions such that f(1) = 2 and g(1) = 6. if h(x) = 5f(x) - 4g(x) + 3x² - 2, what is the value of h(1)?

Answer

Explanation:

Step1: Differentiate ( h(x) )

Using the sum and constant - multiple rules of differentiation. If ( h(x)=5f(x)-4g(x)+3x^{2}-2 ), then ( h^{\prime}(x)=5f^{\prime}(x)-4g^{\prime}(x)+6x ).

Step2: Substitute ( x = 1 )

We know that ( f^{\prime}(1)=2 ) and ( g^{\prime}(1)=6 ). Substitute these values into ( h^{\prime}(x) ): ( h^{\prime}(1)=5\times f^{\prime}(1)-4\times g^{\prime}(1)+6\times1 ) ( h^{\prime}(1)=5\times2-4\times6 + 6) ( h^{\prime}(1)=10-24 + 6) ( h^{\prime}(1)=-8)

Answer:

B. - 8