If f(x) = 3x^2 + 8x, the slope of the tangent to f(x) when x=5 is 38 and the instantaneous rate of change for f(x) is also 38, what would the equation of the line tangent to f(x) when x=5 be?

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Answer 1 · 2017-11-10T20:45:31

#y=38x-75#

Since you know the gradient at 5, and you know the value of #x#, which is 5. Calculate a y value by plugging 5 into:

#y=3x^2+8x#

#y=3(5)^2+8(5)=115#

Equation of a line is : #y= mx +b#

#:.#

#115=38(5)+b=>b=#-75

Equation of tangent line:

#y=38x-75#

Graph:

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