Consider the function $\displaystyle f(x)=3x^2-5x+k$. The equation of the tangent to the graph of $\displaystyle f(x)$ at $\displaystyle x=p$ is $\displaystyle y=7x-9$. Find $\displaystyle p$ and $\displaystyle k$.

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- Jan 27th 2010, 07:35 AMshawliequation of a tangent question
Consider the function $\displaystyle f(x)=3x^2-5x+k$. The equation of the tangent to the graph of $\displaystyle f(x)$ at $\displaystyle x=p$ is $\displaystyle y=7x-9$. Find $\displaystyle p$ and $\displaystyle k$.

- Jan 27th 2010, 07:52 AMDinkydoe
Observe that $\displaystyle f'(p) = y'(p) \Leftrightarrow 6p-5 = 7$

Solve for $\displaystyle p$ and use the fact that $\displaystyle f(p)= 3p^2-5p+k = 7p-9$ to solve for $\displaystyle k$ - Jan 27th 2010, 07:55 AMPulock2009
u must know the following before solving this problem:

1)tangent is nothing but the gradient ie dy/dx=f'(x).

2)for a line y=mx+c the gradient is given by m.

3)the answers are p=2 and k=12.are they correct??? - Jan 27th 2010, 07:57 AMPulock2009
u must know the following before solving this problem:

1)tangent is nothing but the gradient ie dy/dx=f'(x).

2)for a line y=mx+c the gradient is given by m.

3)the answers are p=2 and k=12.are they correct???