maths questions (1 Viewer)

[ta1g]

can someone help me out with working out these questions.

*what angle does the tangent to the curve y=x^4-x^3+7x make with the positive direction of the x-axis at the point where x=2


* find any x values for which the gradient of the tangent to the curve y=x^2-3x-1 is parallel to the line x-2y-1=0

 

[Dreamerish*~]

1. What angle does the tangent to the curve y=x^4-x^3+7x make with the positive direction of the x-axis at the point where x=2

y = x⁴ - x³ + 7x

y' = 4x³ - 3x² + 7x

= x(4x² - 3x + 7)

Wait, before I continue, are you sure you have the signs right? Because it appears we need the quadratics formula.

 

[Dreamerish*~]

2. Find any x values for which the gradient of the tangent to the curve y=x^2-3x-1 is parallel to the line x-2y-1=0

2y = x - 1

y = x/2 - 1/2

. : m = 1/2

y = x² - 3x - 1

y' = 2x - 3

It is parallel to x - 2y - 1 = 0, therefore m = 1/2

1/2 = 2x - 3

1/2 + 3 = 2x

x = 7/4

 

[klaw]

What angle does the tangent to the curve y=x^4-x^3+7x make with the positive direction of the x-axis at the point where x=2

y=x^4-x^3+7x
y'=4x³-3x²+7
When x=2, y'=32-12+7=27

Gradient of tangent=27
Gradient of x axis (y=0)=0

tan @=|[(27-0)/(1)]|
@=88 degrees

 

[s_t_a_r1234]

wherever did u get the 1?

 

[pLuvia]

the formula for crossing lines is

tan@ = m1 - m2 / 1 + m1*m2

i.e. m1 = 27
m2 = 0

27 - 0 / 1 + (27*0)

27 / 1