we know the slope is dy/dx, so at (1,2), the slope is -3.
The tangent line is thus
y-2 = -3(x-1)
y dy = -6x^2 dx
1/2 y^2 = -2x^3 + c
y = √2 √(c-2x^3)
you know that the domain of √ is non-negative numbers, so
c-2x^3 >= 0
2x^3 <= c
x <= ∛(c/2)
The equation dy/dx = -6x^2/y gives the slope at any point on the graph of f(x). The range of f(x) is [0, infinity] and f(1) = 2.
A. Find the equation of the tangent line to f(x) at the point (1,2).
B. Write the function f(x).
C. Determine the domain of the function f(x).
2 answers
To compound off of what Steve said, because the point (1,2) is known, you can plug it into y to get C to be equal to 8. Thus, the domain of the function of would be [-∞, ∛2]. Let me know if you want to see where I got these numbers from
1 answer