if ( f(x)=3 + 3x-5x^{2} ), find ( f^{prime}(3) ).
if ( f(x)=3 + 3x-5x^{2} ), find ( f^{prime}(3) ).
Answer
Explanation:
Step1: Differentiate the function
Differentiate (f(x) = 3+3x - 5x^{2}) term - by - term. Using the power rule (\frac{d}{dx}(x^{n})=nx^{n - 1}) and (\frac{d}{dx}(c)=0) (where (c) is a constant). (f^{\prime}(x)=\frac{d}{dx}(3)+\frac{d}{dx}(3x)-\frac{d}{dx}(5x^{2})) (f^{\prime}(x)=0 + 3-5\times2x) (f^{\prime}(x)=3 - 10x)
Step2: Evaluate the derivative at (x = 3)
Substitute (x = 3) into (f^{\prime}(x)). (f^{\prime}(3)=3-10\times3) (f^{\prime}(3)=3 - 30)
Answer:
(- 27)