calculate the derivative of the following functions at the given point?
f(x)=3x-1 x=17
and
f(x)=-5x^2 x=2
To calculate the derivative of a function at a given point, you can apply the derivative rules and then substitute the given point into the derivative expression.
For the first function, f(x) = 3x - 1, we can calculate its derivative as follows:
Step 1: Apply the Power Rule:
For any function of the form f(x) = ax^n, where "a" is a constant and "n" is a real number, the derivative is given by f'(x) = n * ax^(n-1).
The derivative of f(x) = 3x - 1 will be f'(x) = 3 * 1 * x^(1-1) = 3.
Step 2: Substitute the given point:
To find the derivative at x = 17, substitute the value of x into the derivative expression:
f'(17) = 3.
Therefore, the derivative of f(x) = 3x - 1 at x = 17 is 3.
Now let's move on to the second function, f(x) = -5x^2:
Step 1: Apply the Power Rule:
The derivative of f(x) = -5x^2 can be found using the Power Rule:
f'(x) = 2 * (-5) * x^(2-1) = -10x.
Step 2: Substitute the given point:
To find the derivative at x = 2, substitute the value of x into the derivative expression:
f'(2) = -10(2) = -20.
Therefore, the derivative of f(x) = -5x^2 at x = 2 is -20.