question 2\nif ( f(x)=3 x^{5}-4 x^{2}+3 x + 20 )\nfind the slope of the tangent line at ( x=-1 )\n\nquestion…

question 2\nif ( f(x)=3 x^{5}-4 x^{2}+3 x + 20 )\nfind the slope of the tangent line at ( x=-1 )\n\nquestion 3\n( f(x)=-4 x^{4}+2 x^{3}+2 )\nwhat is the rate of change of ( f(x) ) at ( x=-1 )

question 2\nif ( f(x)=3 x^{5}-4 x^{2}+3 x + 20 )\nfind the slope of the tangent line at ( x=-1 )\n\nquestion 3\n( f(x)=-4 x^{4}+2 x^{3}+2 )\nwhat is the rate of change of ( f(x) ) at ( x=-1 )

Answer

Explanation:

Step1: Differentiate the function

Using the power rule ((x^n)^\prime = nx^{n - 1}), for (f(x)=3x^{5}-4x^{2}+3x + 20), we have (f^\prime(x)=3\times5x^{4}-4\times2x+3\times1+0). So, (f^\prime(x)=15x^{4}-8x + 3).

Step2: Substitute (x = - 1) into the derivative

Substitute (x=-1) into (f^\prime(x)): (f^\prime(-1)=15\times(-1)^{4}-8\times(-1)+3). First, ((-1)^{4}=1), then (15\times1 = 15), (-8\times(-1)=8). So, (f^\prime(-1)=15 + 8+3).

Answer:

(26)