Question

7(x)=4x³-3x²+2x-5, x0=1

Answer 1

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Answer 2

To find the value of the derivative of the function 7(x) = 4x³ - 3x² + 2x - 5 at x = 1, you can follow these steps:

1. Find the derivative of the function 7(x) with respect to x: 7'(x) = d/dx (4x³ - 3x² + 2x - 5)

2. Use the power rule to differentiate each term of the function:

   • For the term 4x³, the derivative is 12x².
   • For the term -3x², the derivative is -6x.
   • For the term 2x, the derivative is 2.
   • The derivative of the constant term -5 is 0.

So, now you have the derivative function: 7'(x) = 12x² - 6x + 2

3. Evaluate the derivative at x = 1: 7'(1) = 12(1)² - 6(1) + 2 7'(1) = 12 - 6 + 2 7'(1) = 8

So, the value of the derivative of 7(x) at x = 1 is 8.