Question
Find the slope of the tangents to the curve y=−x2+5x−6
228
likes1138 views
Answer to a math question Find the slope of the tangents to the curve y=−x2+5x−6
Maude
4.7108 Answers
To find the slope of the tangents to the curve at a particular point, we need to find the derivative of the function y with respect to x.
Given function:y = -x^2 + 5x - 6
Taking derivative of y with respect to x:
\frac{dy}{dx} = \frac{d}{dx} (-x^2 + 5x - 6)
\frac{dy}{dx} = -2x + 5
Now, this gives us the slope of the curve at any point on the curve. So, if we want to find the slope at a specific point, we need to substitute the x-coordinate of that point into the derivative expression.
Therefore, the slope of the tangent to the curvey = -x^2 + 5x - 6 \boxed{-2x + 5}
Note: The slope of the tangent changes depending on the x-coordinate of the point on the curve, as given by the derivative of the function y.
Given function:
Taking derivative of y with respect to x:
Now, this gives us the slope of the curve at any point on the curve. So, if we want to find the slope at a specific point, we need to substitute the x-coordinate of that point into the derivative expression.
Therefore, the slope of the tangent to the curve
Note: The slope of the tangent changes depending on the x-coordinate of the point on the curve, as given by the derivative of the function y.
Frequently asked questions (FAQs)
What is the value of the sine of an angle in a right triangle with an opposite side measuring 30 units and a hypotenuse measuring 50 units?
+
What is the integral of 2x^3 + 5x^2 - 3x + 2 with respect to x?
+
What is the limit of (x^2 - 1)/(x + 1) as x approaches -1?
+
New questions in Mathematics