alleryIf the tangent to the curve $y = e^{2x}$ at point $(a, e^{2a})$ passes through origin, then $a$ equals:
A0
B$1/2$
C1
D$\ln 2$
Answer & Solution
Correct answer: B. $1/2$
Slope at $(a, e^{2a})$: $y' = 2e^{2a}$.
**Tangent:** $y - e^{2a} = 2e^{2a}(x - a)$.
Passes through (0, 0): $-e^{2a} = 2e^{2a}(-a)$
⇒ $1 = 2a$ ⇒ $a = 1/2$.
Keep practising Unit 4-5: Applications of Derivatives & Curve Sketching
Browse all Unit 4-5: Applications of Derivatives & Curve Sketching questions for AP Calculus AB, or explore more Mathematics topics.
Related questions
If $f(x) = x^x$ for $x > 0$, then $f$ has a minimum at $x = $:The function $f(x) = \dfrac{x}{1 + x^2}$ attains its maximum value on $[0, \infty)$ at:Find the **shortest distance** from origin to the curve $xy = 4$ (in the first quadrant):A rectangle is inscribed in a semicircle of radius $R$ with base on the diameter. The **maThe function $f(x) = x^3 - 3x + 1$ has critical points at:$f(x) = 2x^3 - 3x^2 - 12x + 5$. The **local maximum value** occurs at:Find the approximate value of $ qrt{25.5}$ using differentials (given $ qrt{25} = 5$):If $f(x) = x^2 - 4x + 3$, the **interval** on which $f$ is decreasing is: