# Thread: equation of a tangent question

1. ## equation 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 $\displaystyle k$.

2. 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 $\displaystyle k$

3. 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???

4. 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???