Find the slope of the tangent line at point (-2, 2) on the curve 𝑓(𝑥)=2𝑥2+3𝑥.
Question
Find the slope of the tangent line at point (-2, 2) on the curve 𝑓(𝑥)=2𝑥2+3𝑥.
Solution
To find the slope of the tangent line at a given point on the curve, we need to find the derivative of the function, which represents the slope of the tangent line at any point on the curve.
The function is f(x) = 2x^2 + 3x.
Step 1: Find the derivative of the function. The derivative of x^2 is 2x, and the derivative of x is 1. So, the derivative of f(x) is f'(x) = 4x + 3.
Step 2: Substitute the x-coordinate of the given point into the derivative. The x-coordinate of the given point is -2. Substituting -2 into the derivative gives f'(-2) = 4*(-2) + 3 = -8 + 3 = -5.
So, the slope of the tangent line at the point (-2, 2) on the curve is -5.
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