What is the equation of the line tangent to # f(x)=-3x^3 -2x^2 +5# at # x=1#?

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Answer 1 · 2018-05-07T12:59:43

Equation of tangent is #y +13 x = 13 #

# f(x) = -3 x ^3 -2 x^2 + 5 ; x=1 #

# f(1) = -3 -2 + 5 =0 :. f(1)=0 :. # Point is #1,0#

# f(x) = -3 x ^3 -2 x^2 + 5 ; #

# f'(x) = -9 x ^2 -4 x #

# f'(1) = -9 -4 = -13 :. # slope is # -13#

The point is # (1,0)# and slope of tangent is # m= -13#

Equation of tangent is #y-y_1= m(x-x_1)# or

#y-0= -13(x-1) or y = -13 x +13 or y +13 x = 13 # [Ans]