# What is the equation of the tangent line of #f(x)=7x^2+3x# at #x=5#?

The gradient of the tangent to a curve at any particular point is give by the derivative of the curve at that point.

so If

#dy/dx = 14x+3#

When

and

So the tangent we seek passes through

# \ \ \ \ \ y-190=73(x-5) #

# :. y-190=73x-365#

# :. \ \ \ \ \ \ \ \ \ \ y=73x-175 #

We can confirm this solution is correct graphically:

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The equation of the tangent line of f(x)=7x^2+3x at x=5 is y=190x-440.

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