The curve y=x^2-4x+3 has a gradient of -1 at the point where x=a. Find the value of a
Answers
Answer:
given curve y= x^2-4x+3
differentiate wrt x to get gradient,
dy/dx = 2x-4
2a-4= -1
a= 3/2
EXPLANATION.
The curve y = x² - 4x + 3 has a gradient of - 1 at the point where x = a.
Curve : y = x² - 4x + 3.
Differentiate both sides w.r.t x, we get.
⇒ dy/dx = 2x - 4.
Put the value of x = a in the equation, we get.
⇒ dy/dx = 2a - 4.
⇒ 2a - 4 = - 1.
⇒ 2a = - 1 + 4.
⇒ 2a = 3.
⇒ a = 3/2.
∴ The value of a is 3/2.
MORE INFORMATION.
Different forms of the equation of straight line.
(1) Slope - Intercept form : y = mx + c.
(2) Slope point form : The equation of a line with slope m and passing through a point (x₁, y₁) is : (y - y₁) = m(x - x₁).
(3) Two point form : (y - y₁) = [(y₂ - y₁)/(x₂ - x₁)](x - x₁).
(4) Intercept form : x/a + y/b = 1.
(5) Normal (perpendicular) form of line : x cosα + y sinα = p.
(6) Parametric form (distance form) : (x - x₁)/cosθ = (y - y₁)/sinθ = r.