Compute f '(a) algebraically for the given value of a
f(x) = x3 + 8x; a = 7
399
its actually 155 3x^2+8
what is 8 times 16
To compute f'(a) algebraically, we first need to find the derivative of the function f(x) = x^3 + 8x.
Step 1: Differentiate each term of the function separately using the power rule for derivatives. The power rule states that the derivative of x^n is nx^(n-1).
Differentiating the first term: d/dx (x^3) = 3x^(3-1) = 3x^2
Differentiating the second term: d/dx (8x) = 8
Step 2: Combine the derivatives of each term to find the derivative of the entire function.
f'(x) = 3x^2 + 8
Step 3: Substitute the given value of a (a = 7) into the derivative function to get f'(a).
f'(a) = 3a^2 + 8
Substituting a = 7, we can calculate:
f'(7) = 3(7^2) + 8 = 3(49) + 8 = 147 + 8 = 155
Therefore, f'(a) = 155 when a = 7.