# equation of a tangent question

• Jan 27th 2010, 07:35 AM
shawli
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\$.
• Jan 27th 2010, 07:52 AM
Dinkydoe
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 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???
• Jan 27th 2010, 07:57 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???