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Having two real roots is equivalent to having two intersections with the x axis.

The equation is a parabola (a U shape) so, having two real roots is equivalent to having the lowest point ...

1. Set y=a^x2. Take the natural log of both sides: ln(y)=ln(a^x)3. Using the log rules, simplify: ln(y)=xln(a)4. Differentiate both sides with respect to x: 1/y dy/dx=lna+05. Rearrange: dy/dx=yln(a)6. ...

1. Collect like terms on one side: 4x+4x=7-132. Simplify: 8x=-63. Divide to find the solution for x: x=-6/84. Simplify again for the answer: x=-3/4

Differentiation is pretty simple! It has a set of instructions you need to follow and then you should be good to go!

For example, differentiate x^6
The first step is to bring down t...

1. Differentiate the Equation of the curve to find the gradient: y'=3x^2

2. The gradient of the tangent is found by substituting x=1 into y'=3x^2: Gradient of tangent=3

3. N...