Name: Taylor and Maclaurin Series
Uploaded: 2019-07-19
Duration: 9 min 34 s
Description: Let's watch this video to learn about the Taylor series and a special case of those called the Maclaurin series. This uses differentiation and some polynomials

Question

Find the equations of the tangents to the curve

y = 1 + x^{3}

for which the tangent is orthogonal with the line

x + 12 y = 12

.

Accepted Answer

Given curve is $y = 1 + x^{3}$

Slope of tangent to the curve at any point, $\frac{d y}{d x} = \frac{d (1 + x^{3})}{d x}$

$\frac{d y}{d x} = 0 + \frac{d (x^{3})}{d x} = 3 x^{2}$

We have to find tangents orthogonal to the line $x + 12 y = 12$

As required tangents and the given line are perpendicular to each other:

Slope of tangent $\times$ Slope of given line $= - 1$

Slope of tangent $\times \frac{- 1}{12} = - 1$

Slope of tangent $= 12$

$3 x^{2} = 12$

$x^{2} = 4$

$x = 2, x = - 2$

At $x = 2$ , $\Rightarrow y = 1 + x^{3} \Rightarrow y = 1 + 2^{3} \Rightarrow y = 9$

At $x = - 2$ $\Rightarrow y = 1 + x^{3} \Rightarrow y = 1 + {(- 2)}^{3} \Rightarrow y = - 7$

We know that the equation of a line having slope $m$ passing through $(x_{1}, y_{1})$ is

$(y - y_{1}) = m (x - x_{1})$

Equation of tangent: Line having slope $12$ passing through $(2, 9)$ is

$y - 9 = (12) (x - 2)$

$y - 9 = 12 x - 24$

$12 x - y = 15$

line having slope $12$ passing through $(- 2, - 7)$ is

$y - (- 7) = (12) (x - (- 2))$

$y + 7 = 12 x + 24$

$12 x - y = - 17$

Therefore, the equations of the tangents to the curve $y = 1 + x^{3}$ for which the tangent is orthogonal with the line $x + 12 y = 12$ are, $12 x - y = 15 & 12 x - y = - 17$

Find the equations of the tangents to the curve $y = 1 + x^{3}$ for which the tangent is orthogonal with the line $x + 12 y = 12$ .

Important Questions on Applications of Differential Calculus

Learn and Prepare for any exam you want !

Find the equations of the tangents to the curve y=1+x3 for which the tangent is orthogonal with the line x+12y=12.

Important Questions on Applications of Differential Calculus

Learn and Prepare for any exam you want !

Find the equations of the tangents to the curve $y = 1 + x^{3}$ for which the tangent is orthogonal with the line $x + 12 y = 12$ .