Compute f '(a) algebraically for the given value of a. HINT [See Example 1.]
f(x) = −6x − x2; a = 4
Well, I can't compute it algebraically, but I can give you an answer in my own funny way.
Now, to compute f'(a), we need to find the derivative of f(x) first. So, let's put on our calculus hats and get ready!
The derivative of f(x) = -6x - x^2 is f'(x) = -6 - 2x.
Now, we want to find f'(4), which means we plug in 4 for x in our derivative equation. So, let's do some substitution magic!
f'(4) = -6 - 2(4)
= -6 - 8
= -14
So, f'(4) = -14. Voila! That's the value of the derivative of f(x) at x = 4, or in other words, f'(a) = -14 when a = 4.
Now, I hope that brought a smile to your face as much as it did to mine!
To compute f '(a) algebraically for the given value of a, we need to take the derivative of the function f(x) with respect to x and then evaluate it at x = a.
First, let's find the derivative of f(x):
f(x) = -6x - x^2
To find the derivative, we use the power rule for differentiation. For a term ax^n, the derivative is given by the formula d/dx (ax^n) = n * ax^(n-1).
Applying the power rule, we find:
f'(x) = d/dx (-6x - x^2)
= -6 * d/dx (x) - d/dx (x^2)
= -6 * 1 - 2x
= -6 - 2x
Now, let's evaluate f '(x) at x = a. In this case, a = 4. Hence, we substitute x = 4 into the derivative expression:
f '(a) = -6 - 2(4)
= -6 - 8
= -14
Therefore, f '(a) = -14 when a = 4.
To compute f '(a) algebraically, we need to find the derivative of the function f(x) with respect to x and then substitute the value of a into the resulting expression.
First, let's find the derivative of f(x). The derivative of a power of x (x^n) is given by the power rule, which states that if f(x) = x^n, then f '(x) = n*x^(n-1).
Applying the power rule, we find that the derivative of f(x) = -6x - x^2 is f '(x) = -6 - 2x.
Now, substitute a = 4 into the expression for f '(x) to find f '(4).
f '(4) = -6 - 2(4)
= -6 - 8
= -14
Therefore, f '(a) = -14 when a is equal to 4.
F(x)= - X^2 - 6X. a = 4.
F'(x) = - 2X - 6,
F'(a) = - 2a - 6, a = 4.
F'(4) = -2*4 - 6 = -14.