# equation of a tangent question

• January 27th 2010, 08:35 AM
shawli
equation of a tangent question
Consider the function $f(x)=3x^2-5x+k$. The equation of the tangent to the graph of $f(x)$ at $x=p$ is $y=7x-9$. Find $p$ and $k$.
• January 27th 2010, 08:52 AM
Dinkydoe
Observe that $f'(p) = y'(p) \Leftrightarrow 6p-5 = 7$

Solve for $p$ and use the fact that $f(p)= 3p^2-5p+k = 7p-9$ to solve for $k$
• January 27th 2010, 08:55 AM
Pulock2009
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???
• January 27th 2010, 08:57 AM
Pulock2009
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???