hi, i have two questions. Hoepfully someone can help me with them.
1. Find d/dx(x^2)
2. Find the normal to the curve for y=x^3 at the point (1,1).
THANKSS!!!!
i assume if you are asking this they want you to do it by the definition? i don't see why this is so hard for you
recall, $\displaystyle \frac d{dx}x^n = nx^{n - 1}$
or, by the definition, $\displaystyle \frac d{dx}f(x) = \lim_{h \to 0} \frac {f(x + h) - f(x)}h$
step 1: find the slope at x = 1 by finding the derivative of x^3 and plugging in 1 for x (use the rule i told you above).2. Find the normal to the curve for y=x^3 at the point (1,1).
step 2: take the negative inverse of the answer. this gives you the slope for the normal line (since it is perpendicular to the tangent line, whose slope is given by the derivative).
step 3: take this as the value for m, and use the point slope form
$\displaystyle y - y_1 = m(x - x_1)$
where $\displaystyle m$ is the slope of the line, and $\displaystyle (x_1,y_1)$ is a point the line passes through. solve for y and you have your answer