find slope of curve at given point
f (x) = 5x- 3x²
To find the slope of the curve at a given point, we need to find the derivative of the function and evaluate it at that point.
Taking the derivative of f(x) = 5x - 3x² using the power rule and constant rule, we get:
f'(x) = 5 - 6x
Let's say we want to find the slope of the curve at the point (2, f(2)). To do this, we substitute x = 2 into the derivative:
f'(2) = 5 - 6(2) = 5 - 12 = -7
Therefore, the slope of the curve at the point (2, f(2)) is -7.
To find the slope of a curve at a given point, we need to find the derivative of the function and evaluate it at that point. Let's find the derivative of the function f(x) = 5x - 3x² first.
Step 1: Take the derivative of each term separately.
The derivative of 5x is 5.
The derivative of -3x² is -6x.
Step 2: Simplify the derivative expression.
The derivative of f(x) = 5x - 3x² is f'(x) = 5 - 6x.
Now, let's evaluate the derivative at the given point.
If we are given a specific x-value, say x = a, we substitute it into the derivative expression f'(x) = 5 - 6x.
In this case, the given point is not specified, so we cannot evaluate the slope at a particular point without more information.