CBSE (Science) Class 12CBSE
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty

Solution for Write the Equation on the Tangent to the Curve Y = X2 − X + 2 at the Point Where It Crosses the Y-axis ? - CBSE (Science) Class 12 - Mathematics

Login
Create free account


      Forgot password?

Question

Write the equation on the tangent to the curve y = x2 − x + 2 at the point where it crosses the y-axis ?

Solution

When the curve crosses the y-axis, the point on the curve is of the form (0, y).
Here,

\[y = x^2 - x + 2\]

\[ \Rightarrow y = 0 - 0 + 2 = 2\]

\[\text { So, the point where the curve crosses they-axis is }(0, 2).\]

\[\text { Now,} \]

\[y = x^2 - x + 2\]

\[ \Rightarrow \frac{dy}{dx} = 2x - 1\]

\[\text { Slope of the tangent },m= \left( \frac{dy}{dx} \right)_\left( 0, 2 \right) =2\left( 0 \right)-1=-1\]

\[ \therefore \left( x_1 , y_1 \right) = \left( 0, 2 \right)\]

\[\text { and }\]

\[\text { Equation of tangent }\]

\[ = y - y_1 = m\left( x - x_1 \right)\]

\[ \Rightarrow y - 2 = - 1\left( x - 0 \right)\]

\[ \Rightarrow y - 2 = - x\]

\[ \Rightarrow x + y - 2 = 0\]

  Is there an error in this question or solution?
Solution for question: Write the Equation on the Tangent to the Curve Y = X2 − X + 2 at the Point Where It Crosses the Y-axis ? concept: Tangents and Normals. For the courses CBSE (Science), PUC Karnataka Science, CBSE (Arts), CBSE (Commerce)
S
View in app×