find the slope of the curve at a given point y=2x^3 -3x at (-1,1)
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EXPLANATION.
Slope of the curve at a given point.
⇒ y = 2x³ - 3x at point = (-1,1).
As we know that,
⇒ dy/dx = slope of tangent.
⇒ y = 2x³ - 3x.
Differentiate the equation w.r.t x, we get.
⇒ dy/dx = 6x² - 3.
⇒ dy/dx = 6(-1)² - 3.
⇒ dy/dx = 6 - 3.
⇒ dy/dx = 3.
MORE INFORMATION.
Equation of tangent.
(1) = Equation of tangent to the curve y = f(x) at p(x₁, y₁) is.
(y - y₁) = m(x - x₁).
(1) = The tangent at (x₁, y₁) is parallel to x-axes (dy/dx) = 0.
(2) = The tangent at (x₁, y₁) is parallel to y-axes (dy/dx) = ∞.
(3) = The tangent line making equal angles with the axes (dy/dx) = ± 1.
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