The length of tangent to the curvey=x^3-2x^2+4at (2,4) is.......
Answers
Step-by-step explanation:
The curve y = x3 - 2x2 + 4
Differentiating on each side with respect of x.
y' = 3x2 - 4x
Substitute the value x = 2 in above equation.
y' = 3(2)2 - 4(2)
y' = 12 - 8
y' = 8
This is the slope of tangent line to the curve at (2, 4).
To find the tangent line equation, substitute the values of m = 4 and (x, y ) = (2, 4). in the slope intercept form of an equation y = mx + b.
4 = 4(2) + b
b = 4 - 8
b = - 4
Substitute m = 4 and b = - 4 in y = mx + b.
Tangent line is y = 4x - 4
Find the points where the tangent line meets coordinate axis.
Find the intercepts.
Substitute x = 0 in y = 4x - 4
y = 4(0) - 4
y = -4
y intercept is - 4.
Substitute y = 0 in y = 4x - 4
4x - 4 = 0
4x = 4
x = 1
The tangent line meets the x axis at 1 and y axis at - 4.
oxy is a right angle triangle.
Area of right angle triangle = ab/2
a, b are legs of triangle.
a = 1unit , b = 4units
Area of triangle = ab/2
= 1/2(1)(4)
= 4/2
= 2
Area of triangle is 2 square units.