# calculus

posted by .

The slope of a curve is at the point (x,y) is 4x-3. Find the curve if it is required to pass through the point (1,1).

Work...
4(1)-3=1
y-1=1(x-1)
y=x

• calculus -

4x - 3 is your slope, so it is the derivative.

then dy/dx = 4x + 3, integrate to get

y = 2x^2 + 3x + k

plug in (1,1) into that to get k, and you are done!

• calculus -

why would I solve for the constant? I get k=-4. What is meant by curve?

• calculus -

When they say "find the curve" they mean find the equation of function whose graph would be that curve.
your equation y = 2x^2 + 3x - 4 would graph to be a parabola, and a parabola is a curve.

As to the constant, remember that if you differentiate an equation like

y = 2x^2 + 3x - 4
you get y' = 4x + 3 - 0

so when we "anti-differentiate" that we really don't know what the value of the constant was, because its derivative would be zero no matter what the number was.
That is why we include a constant value of c or k to allow for that. Once we sub in the given point we then know the value of that constant

## Similar Questions

1. ### calculus

there are two tangents lines to the curve f(x) = 3x^2 that pass through the point p =0,1 find the x coordinates of the point where the tangents line intersect the curve

1. a.) Find an equation for the line perpendicular to the tangent curve y=x^3 - 9x + 5 at the point (3,5) [* for a. the answer that I obtained was y-5 = -1/18 (x-3) ] b.) What is the smallest slope on the curve?
3. ### calculus

1. Given the curve a. Find an expression for the slope of the curve at any point (x, y) on the curve. b. Write an equation for the line tangent to the curve at the point (2, 1) c. Find the coordinates of all other points on this curve …
4. ### calculus

Consider the curve defined by 2y^3+6X^2(y)- 12x^2 +6y=1 . a. Show that dy/dx= (4x-2xy)/(x^2+y^2+1) b. Write an equation of each horizontal tangent line to the curve. c. The line through the origin with slope -1 is tangent to the curve …
5. ### calculus

A curve passes through the point (1,-11) and it's gradient at any point is ax^2 + b, where a and b are constants. The tangent to the curve at the point (2,-16) is parallel to the x-axis. Find i) the values of a and b ii) the equation …
6. ### Calculus Help Please!!! Check

A curve passes through the point (0, 2) and has the property that the slope of the curve at every point P is three times the y-coordinate of P. Find an equation of the curve. dy/dp = 3y or ∫ (3/y) dy = ∫ dp or 3 ln(y) = …
7. ### Calculus

A curve passes through the point (7,6) and has the property that the slope of the curve at every point P is 4 times the y-coordinate of P. What is the equation of the curve?
8. ### Calculus

The slope of the tangent line to a curve at any point (x, y) on the curve is x/y. What is the equation of the curve if (4, 1) is a point on the curve?
9. ### Calculus

Find the xy-equation of the curve that passes through (-2, -2) and whose slope at any point on the curve is equal to 5 times the x-coordinate of that point
10. ### Calculus

The slope of the tangent to a curve at any point (x, y) on the curve is -x/y . Find the equation of the curve if the point (3,-4) on the curve.

More Similar Questions