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For the function $f(x) = 2x^2 −5x$, determine the gradient of the tangent to the curve at the point $x = 6$.
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By differentiation, gradient of curve = df/dx = 2(2x) - 5 = 4x - 5

At the point x = 6, gradient of curve = 4x - 5 = 4(6) - 5 = 19

But at a given point on a curve, the gradient of the curve is equal to the gradient of the tangent to the curve.

Therefore the gradient of the tangent to the curve at x = 6 is equal to the gradient of the curve at that point = 19.
by Diamond (39,246 points)

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