Answer:
The gradient for the function 4x³ + 13x when x is 2 is 61.
Step-by-step explanation:
Before we do anything, let's find the partial derivative of 4x³ + 13x.
d/dx (4x³ + 13x)
Step 1:The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of axⁿ is naxⁿ⁻¹.
3 * 4x³⁻¹ + 13x¹⁻¹
Step 2: Multiply 3 and 4.
12x³⁻¹ + 13x¹⁻¹
Steps 3 & 4: Subtract 1 from 3 (Step 3) and 1 (Step 4) respectively.
12x² + 13
Note: 13x⁰ simply becomes 13 because t⁰ = t.
Now that we know the derivative, substitute x for 2.
12(2²) + 13
Step 5: Square 2 to get 4.
12(4) + 13
Step 6: Multiply 12 and 4 to get 48.
48 + 13
Step 7: Add 48 and 13 to get 61.
61
So, the gradient of 4x³ + 13x is 61, if x is 2.
