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Default Calculus - 02-12-2012, 09:05 PM

I would be most appreciative if someone would explain this step by step plawks.

Prawblum:

Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line.

f(x) = 6x-3x^2 at (-2,-24)

m=___

y=___


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Default 02-20-2012, 10:52 PM

1. m = gradient. To find the gradient, differentiate f(x)

i.e. f'(x) = 6 - 6x *because f'(x) = m*


2. To find m at the given point, simply substitute x= -2 into f'(x)

i.e. f'(x) = 6 - 6(-2) = 18

To determine the equation, use the formula (y-y1) = m(x-x1)

i.e. y1 = -24; x1 = -2, m = 18 (from 2)

(y-[-24]) = 18(x-[-2])
y+24 = 18(x+2)
y+24 = 18x + 36
y = 18x + 36 - 24
y = 18x + 12

  
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