Question

Пряма y=-3/4x+c є дотичною до лінії заданої рівнянням y=0,5x^4-x. Знайти абсцису точки дотику.

Answer 1

$y_1=- \frac{3}{4} x+c$     та    $y_2=0,5x^4-x$
Знайдемо похідні й приравняeмo.
$y_1`=- \frac{3}{4}$ i $y_2=2x^3-1$
(кутовий коефіцієнт прямої дорівнює тангенсу кута нахилу дотичної)
$2x^3-1=- \frac{3}{4}$
$x^3=\frac{1}{8}$
$x=\frac{1}{2}$ - абсциса точки дотику

Answer 2

Finding the Point of Tangency

To find the abscissa (x-coordinate) of the point of tangency between the line y = -3/4x + c and the curve y = 0.5x^4 - x, we need to set the two equations equal to each other and solve for x.

Setting the equations equal to each other, we have:

-3/4x + c = 0.5x^4 - x

To simplify the equation, let's multiply everything by 4 to eliminate the fraction:

-3x + 4c = 2x^4 - 4x

Rearranging the equation to bring all the terms to one side, we get:

2x^4 - 4x + 3x - 4c = 0

Combining like terms, we have:

2x^4 - x - 4c = 0

Now, we can solve this equation to find the values of x.

Unfortunately, I couldn't find any specific information or formulas to solve quartic equations in the search results. However, there are various methods to solve quartic equations, such as factoring, using the rational root theorem, or using numerical methods like Newton's method.

If you have the specific value of c, we can substitute it into the equation and solve for x using numerical methods or approximation techniques.