Slope of Tangent Lines Calculator

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Example

Created on 2024-06-20Asked by Chloe Walker (Solvelet student)

Find the slope of the tangent line to the curve

y = x^2 - 3x + 2

at the point

x = 1

Solution

To find the slope of the tangent line to the curve

y = x^2 - 3x + 2

at the point

x = 1

: 1. **Compute the derivative of

y

:**

\frac{dy}{dx} = 2x - 3.

2. **Evaluate the derivative at

x = 1

:**

\frac{dy}{dx}\Bigg|_{x=1} = 2(1) - 3 = -1.

3. **Result:** The slope of the tangent line at

x = 1

-1

. Solved on Solvelet with Basic AI Model

Some of the related questions asked by Layla Lee on Solvelet

1. Find the equation of the tangent line to the curve

y = x^2

at the point

(1, 1)

.2. Determine the slope of the tangent line to the curve

y = \ln(x)

at the point

(e, 1)

DefinitionThe slope of a curve passing through that point is obtained by dividing its space by the change in its value. What it means is in a function is the derivative of that function. Example: A more permanent pattern for f(x) = x ^ 2 is f ʹ( x ) = 2 x. Therefore, 3 slope for this graph at point x = f(3) = f ʹ(3) = 2× 3 = 6.

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