If the tangent line to y = f(x) at (4, 3) passes through the point (0, 2), find

EunoR 2021-10-29 Answered
If the tangent line to y = f(x) at (4, 3) passes through the point (0, 2), find f(4) and f’(4)

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

yagombyeR
Answered 2021-10-30 Author has 23648 answers
The tangent to y=f(x) at (4,3)
This suggest that \(\displaystyle{\left({4},{3}\right)}\) is a point on the graph of y=f(x)
Therefore, \(\displaystyle{f{{\left({4}\right)}}}={3}\)
Slope of the tangent at x=4 to y=f(x) is f'(4)
Since the tangent passes through (4,3) and (2,0), its slope is equal to
\(\displaystyle{m}={\frac{{{2}-{3}}}{{{0}-{4}}}}={\frac{{-{1}}}{{{4}}}}={0.25}\)
This is equal to f'(4)
Result: f(4)=3 and f'(4)=0.25
Not exactly what you’re looking for?
Ask My Question
0
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-09-15

Find sets of parametric equations and symmetric equations of the line that passes through the given point and is parallel to the given vector or line. (For each line, write the direction numbers as integers.)
Point: (-3, 4, 5)
Parallel to: \(\displaystyle\frac{{{x}-{1}}}{{2}}=\frac{{{y}+{1}}}{ -{{3}}}={z}-{5}\)
(a) Parametric equations
(b) Symmetric equations

asked 2021-09-10
Write the equation of the line tangent to \(\displaystyle{f{{\left({x}\right)}}}={\tan{{x}}}+{3}\) at \(\displaystyle{\left(\frac{\pi}{{4}}.{4}\right)}\)
asked 2021-12-05
Find parametric equations for the line that passes through the point
\(\displaystyle{P}{\left(-{3},\ {7},\ {9}\right)}\) and \(\displaystyle{Q}{\left({4},\ {1},\ -{5}\right)}\)
asked 2021-12-02
Find parametric equations for the line that passes through the point \(\displaystyle{\left({5},\ {2}\right)}\) and is parallel to the line
\(\displaystyle{y}={\frac{{-{7}}}{{{2}}}}{x}-{2}\)
asked 2021-06-04
Find an equation of the plane tangent to the following surface at the given point.
\(7xy+yz+4xz-48=0;\ (2,2,2)\)
asked 2021-09-03

\(P(3,-4,-1)\) passing through point \(v=i+j+k\).
Write the parametric equation of the line parallel to its vector

asked 2021-12-04
Find parametric equation of the line passing through point \(\displaystyle{\left({4},\ {2}\right)}\) parallel to vector
\(\displaystyle\vec{{{v}}}=-\hat{{{i}}}+{5}\hat{{{j}}}\)
...