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Find the equation of the tangent to curve y = 5x2+6x+7  at the point (1/2, 35/4).

Solution :

The equation of the given curve is

y = 5x2+6x+7

dydx = -10x + 6

(dydx)(1/2,35/4) = 104 + 6 = 1

The required equation at (1/2, 35/4) is

y – 354 = (dydx)(1/2,35/4) (x12)

y – 35/4 = 1(x – 1/2)

Equation of tangent is y = x + 33/4


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