Advertisements
Advertisements
प्रश्न
Find the equation of tangent and normal to the following curve.
y = x3 - x2 - 1 at the point whose abscissa is -2.
उत्तर
Equation of the curve is y = x3 - x2 - 1 ...(i)
Differentiating w.r.t. x, we get
`"dy"/"dx" = 3"x"^2 - 2"x"`
If x = - 2, ....[Given]
Putting the value of x in (i), we get
y = (- 2)3 - (- 2)2 - 1 = - 8 - 4 - 1 = - 13
∴ Point is P (x1, y1) ≡ (-2, -13)
Slope of tangent at (- 2,- 13) is
`("dy"/"dx")_((-2, -13)` = 2(-2)2 - 2(-2) = 12 + 4 = 16
Equation of tangent at (- 2, -13) is
y - y1 = `("dy"/"dx")_(("x" = -2)` (x - x1)
∴ y - (- 13) = 16 [x - (- 2)]
∴ y + 13 = 16x + 32
∴ 16x - y + 19 = 0
Slope of normal at (- 2, - 13) is `(-1)/("dy"/"dx")_((-2, -13)` = `- 1/16`
Equation of normal at (-2, - 13) is
∴ y + 13 = `(-1)/16`(x + 2)
∴ x + 16y + 210 = 0
APPEARS IN
संबंधित प्रश्न
Find the derivative of the following function from first principle.
`1/x^2`
Find the derivative of the following function from first principle.
`(x+1)/(x -1)`
Find the derivative of the following function from first principle:
−x
Find the derivative of the following function from first principle:
(–x)–1
Find the derivative of the following function from first principle:
sin (x + 1)
Find the equations of tangent and normal to the curve y = 3x2 - 3x - 5 where the tangent is parallel to the line 3x − y + 1 = 0.
Choose the correct alternative.
The equation of tangent to the curve x2 + y2 = 5 where the tangent is parallel to the line 2x – y + 1 = 0 are
Choose the correct alternative.
If elasticity of demand η = 1, then demand is
Choose the correct alternative.
If f(x) = 3x3 - 9x2 - 27x + 15 then
Fill in the blank:
If f(x) = x - 3x2 + 3x - 100, x ∈ R then f''(x) is ______
Fill in the blank:
If f(x) = `7/"x" - 3`, x ∈ R x ≠ 0 then f ''(x) is ______
State whether the following statement is True or False:
The equation of tangent to the curve y = 4xex at `(-1, (- 4)/"e")` is ye + 4 = 0
State whether the following statement is True or False:
x + 10y + 21 = 0 is the equation of normal to the curve y = 3x2 + 4x - 5 at (1, 2).
Find the equation of tangent and normal to the following curve.
y = x2 + 4x at the point whose ordinate is -3.
Choose the correct alternative:
Slope of the normal to the curve 2x2 + 3y2 = 5 at the point (1, 1) on it is
State whether the following statement is True or False:
The equation of tangent to the curve y = x2 + 4x + 1 at (– 1, – 2) is 2x – y = 0
Find the equation of tangent and normal to the curve y = x2 + 5 where the tangent is parallel to the line 4x – y + 1 = 0.
y = ae2x + be-3x is a solution of D.E. `(d^2y)/dx^2 + dy/dx + by = 0`
Find the equations of tangent and normal to the curve y = 6 - x2 where the normal is parallel to the line x - 4y + 3 = 0
