How do you find the equation of a line tangent to the function #y=x^2-x-6# at (3,0)?

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Answer 1 · 2018-02-07T22:11:45

#y = 5x - 15#

#y = x^2 - x - 6#

gradient of tangent line #= (Deltay)/(Deltax) (x^2-x-6)#

power rule: #(Deltay)/(Deltax) (x^n) = nx^(n-1)#

#(Deltay)/(Deltax) (x^2-x-6) = 2x^1 - 1^0 +- 0#

#= 2x - 1#

at #(x,y)#, the gradient of the tangent line is #2x - 1#.

when #x = 3#, #2x - 1 = 5#

gradient of tangent line at #(3,0): 5#

#y = mx + c#

#y = 5x + c#

#0 = (5*3) + c#

#0 = 15 + c#

#0 = 15 - 15#

#m = 5, c = -15#

#y = 5x - 15#